Temporal fluctuations in coherence of brain waves.

As a measure of dynamical structure, short-term fluctuations of coherence between 0.3 and 100 Hz in the electroencephalogram (EEG) of humans were studied from recordings made by chronic subdural macroelectrodes 5-10 mm apart, on temporal, frontal, and parietal lobes, and from intracranial probes deep in the temporal lobe, including the hippocampus, during sleep, alert, and seizure states. The time series of coherence between adjacent sites calculated every second or less often varies widely in stability over time; sometimes it is stable for half a minute or more. Within 2-min samples, coherence commonly fluctuates by a factor up to 2-3, in all bands, within the time scale of seconds to tens of seconds. The power spectrum of the time series of these fluctuations is broad, extending to 0.02 Hz or slower, and is weighted toward the slower frequencies; little power is faster than 0.5 Hz. Some records show conspicuous swings with a preferred duration of 5-15s, either irregularly or quasirhythmically with a broad peak around 0.1 Hz. Periodicity is not statistically significant in most records. In our sampling, we have not found a consistent difference between lobes of the brain, subdural and depth electrodes, or sleeping and waking states. Seizures generally raise the mean coherence in all frequencies and may reduce the fluctuations by a ceiling effect. The coherence time series of different bands is positively correlated (0.45 overall); significant nonindependence extends for at least two octaves. Coherence fluctuations are quite local; the time series of adjacent electrodes is correlated with that of the nearest neighbor pairs (10 mm) to a coefficient averaging approximately 0.4, falling to approximately 0.2 for neighbors-but-one (20 mm) and to < 0.1 for neighbors-but-two (30 mm). The evidence indicates fine structure in time and space, a dynamic and local determination of this measure of cooperativity. Widely separated frequencies tending to fluctuate together exclude independent oscillators as the general or usual basis of the EEG, although a few rhythms are well known under special conditions. Broad-band events may be the more usual generators. Loci only a few millimeters apart can fluctuate widely in seconds, either in parallel or independently. Scalp EEG coherence cannot be predicted from subdural or deep recordings, or vice versa, and intracortical microelectrodes show still greater coherence fluctuation in space and time. Widely used computations of chaos and dimensionality made upon data from scalp or even subdural or depth electrodes, even when reproducible in successive samples, cannot be considered representative of the brain or the given structure or brain state but only of the scale or view (receptive field) of the electrodes used. Relevant to the evolution of more complex brains, which is an outstanding fact of animal evolution, we believe that measures of cooperativity are likely to be among the dynamic features by which major evolutionary grades of brains differ.

The microwave background anisotropies: Observations

Most cosmologists now believe that we live in an evolving universe that has been expanding and cooling since its origin about 15 billion years ago. Strong evidence for this standard cosmological model comes from studies of the cosmic microwave background radiation (CMBR), the remnant heat from the initial fireball. The CMBR spectrum is blackbody, as predicted from the hot Big Bang model before the discovery of the remnant radiation in 1964. In 1992 the cosmic background explorer (COBE) satellite finally detected the anisotropy of the radiation—fingerprints left by tiny temperature fluctuations in the initial bang. Careful design of the COBE satellite, and a bit of luck, allowed the 30 μK fluctuations in the CMBR temperature (2.73 K) to be pulled out of instrument noise and spurious foreground emissions. Further advances in detector technology and experiment design are allowing current CMBR experiments to search for predicted features in the anisotropy power spectrum at angular scales of 1° and smaller. If they exist, these features were formed at an important epoch in the evolution of the universe—the decoupling of matter and radiation at a temperature of about 4,000 K and a time about 300,000 years after the bang. CMBR anisotropy measurements probe directly some detailed physics of the early universe. Also, parameters of the cosmological model can be measured because the anisotropy power spectrum depends on constituent densities and the horizon scale at a known cosmological epoch. As sophisticated experiments on the ground and on balloons pursue these measurements, two CMBR anisotropy satellite missions are being prepared for launch early in the next century.

Linear and nonlinear pathways of spectral information transmission in the cochlear nucleus

At the level of the cochlear nucleus (CN), the auditory pathway divides into several parallel circuits, each of which provides a different representation of the acoustic signal. Here, the representation of the power spectrum of an acoustic signal is analyzed for two CN principal cells—chopper neurons of the ventral CN and type IV neurons of the dorsal CN. The analysis is based on a weighting function model that relates the discharge rate of a neuron to first- and second-order transformations of the power spectrum. In chopper neurons, the transformation of spectral level into rate is a linear (i.e., first-order) or nearly linear function. This transformation is a predominantly excitatory process involving multiple frequency components, centered in a narrow frequency range about best frequency, that usually are processed independently of each other. In contrast, type IV neurons encode spectral information linearly only near threshold. At higher stimulus levels, these neurons are strongly inhibited by spectral notches, a behavior that cannot be explained by level transformations of first- or second-order. Type IV weighting functions reveal complex excitatory and inhibitory interactions that involve frequency components spanning a wider range than that seen in choppers. These findings suggest that chopper and type IV neurons form parallel pathways of spectral information transmission that are governed by two different mechanisms. Although choppers use a predominantly linear mechanism to transmit tonotopic representations of spectra, type IV neurons use highly nonlinear processes to signal the presence of wide-band spectral features.

Spectrum of 100-kyr glacial cycle: Orbital inclination, not eccentricity

Spectral analysis of climate data shows a strong narrow peak with period ≈100 kyr, attributed by the Milankovitch theory to changes in the eccentricity of the earth’s orbit. The narrowness of the peak does suggest an astronomical origin; however the shape of the peak is incompatible with both linear and nonlinear models that attribute the cycle to eccentricity or (equivalently) to the envelope of the precession. In contrast, the orbital inclination parameter gives a good match to both the spectrum and bispectrum of the climate data. Extraterrestrial accretion from meteoroids or interplanetary dust is proposed as a mechanism that could link inclination to climate, and experimental tests are described that could prove or disprove this hypothesis.